After figuring out the math again, the outlook for the USA to advance to the semifinals in the event of a Japan win over Korea Wednesday night is not good.

If Japan wins, the best the USA can get is a three-way tie at 2-1.

Tiebreaker #1 is head-to-head - Everybody would be 1-1.
Tiebreaker #2 is runs allowed per inning played on defense - The USA total is stuck now at 10 runs in 17 innings (the USA only pitched 8 innings against Korea) or .58. Korea is at 3 in 9 innings of defense for .33. Japan is at 4 in 8 2/3 innings which is at .46.

So if Japan beats Korea, but scores no more than 6 runs and it's a nine-inning game, you get:

USA at .588 (10 runs in 17 innings)

Korea at .529 (9 runs in 17 innings, since Korea would play only 8 Wednesday)

Japan would be no greater than .509 (9 runs in 17 2/3 innings)

If it's a 7-6 win for Japan and the game is decided in the ninth and Korea gets one or two outs before Japan scores the winning run, then the USA would also be eliminated. Or it could be 8-7, see below.

If the game goes into extra innings, there are a whole world of problems for Team USA.

So, if you're pulling for Team USA, then you need to root for Korea Wednesday night. Big time.

Update -- AP stories say that the USA will be eliminated if Japan wins by scoring SEVEN or fewer runs instead of six. However, like an angry math teacher, I would like the people to show their work. If Japan were to score seven in nine innings, then Korea would have surrendered 10 runs in 17 innings, just like the U.S. Then the next tiebreaker, which would be earned runs would come into play. The USA has surrendered 10 earned runs. So far, only Japan has given up an unearned run. So if anyone can explain to me why seven runs is the magic number to eliminate and not six, I'd be glad to find out.

Please show your work for full credit.

The first person to show me definitive proof before I leave to go to Anaheim will win a WBC souvenir of my choosing. Although you can pick the country, subject to availability at the souvenir stands in Anaheim.

Is it possible that Korea's win over the US would come into play after the runs allowed tiebreaker sent Japan to the next round?

Head-to-head won't work in the initial 3-way tie, so runs allowed is used to break the tie. Now there's a 2-way tie... do you continue to the next tiebreaker (earned runs/inning) or start over using head-to-head?

More of a question than an answer, I guess... and I neglected to show my work.

The tiebreaker rules don't say that you remove one team from the mix and then work it out as a two-way tie (like the NFL does)
 Ties shall be broken in the following order of priority:
 The team that defeated the other tied team head-to-head in a given Round shall be ranked higher in the pool standings for such Round.
 The tied teams shall be ranked in the standings for that Round according to fewest runs allowed divided by the number of innings (including partial innings) played in defense in the games in that Round between the teams tied.
 The tied teams shall be ranked in the standings according to fewest earned runs allowed divided by the number of innings (including partial innings) played in defense in the games in that Round between the teams tied.
 The tied teams shall be ranked in the standings according to highest batting average in games in that Round between the teams tied.
 Standings shall be determined by the drawing of lots, conducted by WBCI.

1 No, I think they continue to the next tiebreaker. Otherwise, the US would have been #1 in its pool and Mexico #2, because the US beat Mexico, but because they were both in a 3-way tie with Canada, that fact didn't matter - they just move on to the next tiebreaker.

My guess is that as teams "win" or pass a tiebreaker, they are no longer considered "tied teams" in the next tiebreaker rule. So the "math" would look like this:

1. Head-to-head: Everyone is tied

2. Runs allowed: If Japan wins 7-6 over Korea, Japan is through to the next round by virtue of giving up only 10 runs in 17 2/3 innings (against 10 runs in 17 innings for both US and Korea).

3. Earned runs allowed: At this point, since Japan is definitely though (due to tiebreak #2), the US and Korea are the only remaining "tied teams". Therefore, Korea wins the tiebreak by virtue of its 7-3 win over the US (the only "games between the teams tied"). That is, Korea will have given up 3 runs in 9 innings, whereas the US has given up 7 runs in 8 innings.

That's my best guess, although it's just a guess. Who comes up with these rules anyway? Can't we get an RPI? Where's a good panel of voting coaches when you need one?

3 My understanding is no, Korea is not through no matter what. At least, not yet. If they give up 7 runs or more to Japan and lose the game, they will fall into the tiebreaker, assuming the US beats Mexico.

Cuba finished first in the other pool and drew the #4 team in the other group, which was the USA. The Netherlands was #2 and got the #3 team in the other group Puerto Rico. The other matchups were Panama vs Nicaragua and Korea vs Japan.

The other pool had no ties.

Among the three tied teams:
Nicaragua beat the U.S. 14-2, but lost to Puerto Rico 6-5
Puerto Rico beat Nicaragua 6-5 and lost to the US 12-6.
The US lost to Nicaragua 14-2, but beat Puerto 12-6.

So they were all 1-1.
Nicaragua gave up 8 runs
Puerto Rico gave up 17 runs
The USA gave up 20 runs

If it's a 7-6 win for Korea and the game is decided in the ninth and Korea gets one or two outs before losing, then the USA would also be eliminated.

Ok, this sentence is throwing me for a loop. How can Korea win 7-6 and then get one or two outs and lose? Do you mean "lead" instead of "win"? If Korea wins, all we need to do is beat Mexico, right??
vr, Xei

Do they really count 1/3 and 2/3 innings when a home team wins in the bottom of the ninth?

I sat down and my math supports Bob's and not AP's. If Japan scores 7 runs in tonight's game in 9 innings, they will have 11 runs allowed over 18 innings, or 0.611/ 9 innings, compared to the US's 0.588. If Japan's runs were allowed over 17 2/3 innings, its ratio is even higher, 0.623. Either way, the US would win the tie-breaker.

If Japan scores 6 runs in 9 innings, they will have allowed 10 runs in 18 innings, or 0.556/ 9 innings, or 12 runs over 17 2/3 innings, or 0.566. Either way, Japan would win the tie-breaker.

What I've gotten out of all of this is that the tiebreakers are way too complicated and everything will be much easier if Korea beats Japan and the US beats Mexico. Preferrably both games will be huge blowouts.

Therefore, this is the scenario I'm cheering for, tiebreakers be damned.

Sorry, I got confused between runs scored and runs allowed. Change "Japan scores" to "Japan allows" in my earlier post and it should be correct.

The AP is now saying the US will be eliminated if Japan wins and allows South Korea five or fewer runs: http://news.yahoo.com/s/ap/20060315/ap_on_sp_ba_ne/bbi_classic_4

As Bob said, Korea could allow Japan to score up to 7 runs and still be tied with the US according to the runs allowed tie-breaking rules (10 runs allowed over 17 innings).

But it also seems that if Japan wins and scores 8 runs or more, while limiting South Korea to 5 or fewer runs, South Korea could be eliminated under the tie-breaking formula as long as the US wins on Thursday.

I know the WBC is following historical precedent in using runs allowed and earned runs allowed per inning, but is there some rationale I am missing for not using run difference per inning instead, similar to what they do in soccer? Why completely ignore the offensive side of the game in the tiebreak?